Problem $2$

$[$From Hillier and Liberman, $8$e$]$

Ian loves steaks and potatoes. Therefore, he has decided to go on a steady diet of only these two

foods $($plus some liquids and vitamin supplements$)$ for all his meals. Ian realizes that this isn$$t the

healthiest diet, so he wants to make sure that he eats the right quantities of the two foods to satisfy

some key nutritional requirements. He has obtained the following nutritional and cost information:

Ingredient

Grams of Ingredient per Serving Daily

Requirement

$($Grams$)$

Steak Potatoes

Carbohydrates $69>=75$

Protein $198\mathrm{.}5>=40$

Fat

Cost per Serving $$18$ $$6$

Ian wishes to determine the number of daily servings $($may be fractional$)$ of steak and potatoes that

will meet these requirements at a minimum cost. Can you help Ian with his problem using a linear

programming model? Here are the questions for you:

$2$a$)$ Define the decision variables of Ian$$s diet model as completely as you can.

$2$b$)$ Write the objective function for this model.

$2$c$)$ Write all constraints of the model.Ian loves steaks and potatoes. Therefore, he has decided to go on a steady diet of only these two foods $($plus some liquids and vitamin supplements$)$ for all his meals. lan realizes that this isn't the healthiest diet, so he wants to make sure that he eats the right quantities of the two foods to satisfy some key nutritional requirements. He has obtained the following nutritional and cost information:

$\backslash$table$[[,$Grams of Ingredient per Serving,$\backslash$table$[[$Daily$],[$Requirement$]]],[$Ingredient$,$Steak,Potatoes,$($Grams$)],[$Carbohydrates$,6,9,75$